Expand the Logarithmic Expression natural log of 1/(x^2)

$\ln (\frac{1}{x^{2}})$

Rewrite $\ln (\frac{1}{x^{2}})$ as $\ln (1) - \ln (x^{2})$ .

$\ln (1) - \ln (x^{2})$

Expand $\ln (x^{2})$ by moving $2$ outside the logarithm.

$\ln (1) - (2 \ln (x))$

The natural logarithm of $1$ is $0$ .

$0 - (2 \ln (x))$

Subtract $2 \ln (x)$ from $0$ .

$- (2 \ln (x))$

Multiply $2$ by $- 1$ .

$- 2 \ln (x)$